Phase functions

Tabulated phase function (irregular angular grid) (tabphase_irregular)

Parameter	Type	Description	Flags
values	string	A comma-separated list of phase function values parameterized by the cosine of the scattering angle. Must have the same length as nodes.	P
nodes	string	A comma-separated list of \(\cos \theta\) specifying the grid on which values are defined. Bounds must be [-1, 1] and values must be strictly increasing. Must have the same length as values.	P

This plugin implements a generic phase function model for isotropic media parameterized by a lookup table giving values of the phase function as a function of the cosine of the scattering angle.

This plugin is a variant of the tabphase plugin and behaves similarly but uses an irregular distribution internally. Consequently, tabphase performs better for evaluation and sampling.

Rayleigh phase function (rayleigh_polarized)

Parameter	Type	Description	Flags
depolarization	float	Depolarization factor, the ratio of intensities parallel and perpendicular to the plane of scattering for light scattered at 90°.	P ∂

Scattering by particles that are much smaller than the wavelength of light (e.g. individual molecules in the atmosphere) is well-approximated by the Rayleigh phase function.

Lookup table (polarized) phase function (tabphase_polarized)

Parameter	Type	Description	Flags
m11	string	A comma-separated list of phase matrix coefficient 1,1 of the phase function, parametrized by the cosine of the scattering angle.	P
m12	string	A comma-separated list of phase matrix coefficient 1,2 of the phase function, parametrized by the cosine of the scattering angle.	P
m22	string	A comma-separated list of phase matrix coefficient 2,2 of the phase function, parametrized by the cosine of the scattering angle.	P
m33	string	A comma-separated list of phase matrix coefficient 3,3 of the phase function, parametrized by the cosine of the scattering angle.	P
m34	string	A comma-separated list of phase matrix coefficient 3,4 of the phase function, parametrized by the cosine of the scattering angle.	P
m44	string	A comma-separated list of phase matrix coefficient 4,4 of the phase function, parametrized by the cosine of the scattering angle.	P
nodes	string	A comma-separated list of \(\cos \theta\) specifying the grid on which values are defined. Bounds must be [-1, 1] and values must be strictly increasing. Must have the same length as values.	P

This plugin implements a generic phase function model for isotropic media parametrized by a lookup table giving values of the phase function as a function of the cosine of the scattering angle.

Notes

• The scattering angle cosine is here defined as the dot product of the incoming and outgoing directions, where the incoming, resp. outgoing direction points toward, resp. outward the interaction point.

• From this follows that \(\cos \theta = 1\) corresponds to forward scattering.

• Lookup table points are regularly spaced between -1 and 1.

• Phase function values are automatically normalized.

• For polarized phase functions, this assumes (for the time being) the structure of a phase function with spherically symmetric particles, i.e. there are only four unique elements of the Mueller matrix: M_{11}, M_{12}, M_{33}, and M_{34}